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Numerade Educator

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Problem 47 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = \left( 1+ \frac {2}{n} \right)^n $

Answer

Converges

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Video Transcript

for this problem, we just have tio recall a certain serum, so recall that either the ex can be written as limit as n goes to infinity of one plus X over in to the end. And as long as you're familiar with this, the're, um then this problem is fairly straightforward. This is just limit as n goes to infinity of one plus two over in to the end. So the same thing that's happening here except instead of an ex we have to. Which means that this should be equal to e to the power of two. So we have convergence and it converges to e squared.